How to abstract away the interface to two similar classes?

I'm writing an Ultimate Tic-Tac-Toe engine as a programming exercise (for myself, not homework) and I have two similar classes. One is a class MiniBoard that contains a single normal Tic-Tac-Toe board, and another Board that is itself a large Tic-Tac-Toe board conisiting of 9 MiniBoards, one for each large cell in the game.

I also have a function int getState( ... ) that returns a certain number depending on whether a board is won, lost, drawn or in-progress. Since there is obvious symmetry between MiniBoard and Board it appears to me that I should be able to make my getState function accept both MiniBoard and Board as an argument, afterall they both must be either won, drawn, lost or in-progress.

At first I thought to make Board inherit from MiniBoard, but this approach turned out unnecessarily complicated because the functionality of MiniBoard is fundamentally different from Board, even though they do represent very similar objects. It also doesn't really follow the "IS A" relationship of OOP inheritance.

The idea that I currently have, but don't know if is any good, is to make an abstract base class BaseBoard that defines the common properties and methods as virtual and then have Board and MiniBoard derive from BaseBoard. Then I would define my function for getting the state as:

int getState(const BaseBoard &board)

The main issue I have with this approach is that I don't know upfront what kinds of properties and methods will I need for my BaseBoard down the line. And if I ever get the the point of having a large chain of inheritance that starts with BaseBoard and wanting to change something, that would mean I would have to change every class definition down the chain of inheritance. What is the solution to this issue? Just derive more classes?

All in all, is this a good way to solve the problem? And what are the pros and cons? I'm not very familiar with abstract base classes in C++. Any help is appreciated.